Let a random experiment be the cast of a pair of unbiased dice,each having six f
ID: 2951860 • Letter: L
Question
Let a random experiment be the cast of a pair of unbiased dice,each having six faces and let the random variable X denote the sum of the dice. a) with reasonable assumptions determine the p.m.f. f(x). Hint: Picture the sample space consisting of the 36 points.(result on the first die, result on second die), and assumethat each has probability 1/36. Find the probability for each possible outcome of X, namelyx=2,3,4,...12. b) Draw the bar graph for f(x). random variable X denote the sum of the dice. a) with reasonable assumptions determine the p.m.f. f(x). Hint: Picture the sample space consisting of the 36 points.(result on the first die, result on second die), and assumethat each has probability 1/36. Find the probability for each possible outcome of X, namelyx=2,3,4,...12. b) Draw the bar graph for f(x).Explanation / Answer
To find the Probability Mass Function. a.) Lets call dice 1 a and dice 2 b. Such that I canrefer to them as (a, b) where a and b is the number on top of thefirst and second die respectively. So a and b can be anyinteger from 1 to 6. The best way to see this visually I think is to simply list all thepossibilities as the directions state there are 36: (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) Each diagonal is represents the possibility of that sumoccurring. For example, 2 has a 1/36 chance, 4 has a 3/36chance. I just used symmetric colors on both sides of thegraphs because I ran out of colors, but the diagonals are all thatmatter here. Using those probabilities for each sum, you have are your pointsfor the bar graph. If X = the sum of the dice. X rangesfrom [2-12] and f(X) from 1/36 to 6/36. This should be plentyof information to determine the rest of the problem.
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